Data commit

Task/Set/Maxima/set.maxima

@@ -0,0 +1,78 @@
+/* illustrating some functions on sets; names are self-explanatory */
+
+a: {1, 2, 3, 4};
+{1, 2, 3, 4}
+
+b: {2, 4, 6, 8};
+{2, 4, 6, 8}
+
+intersection(a, b);
+{2, 4}
+
+union(a, b);
+{1, 2, 3, 4, 6, 8}
+
+powerset(a);
+{{}, {1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 4}, {1, 3}, {1, 3, 4}, {1, 4}, {2}, {2, 3}, {2, 3, 4}, {2, 4}, {3}, {3, 4}, {4}}
+
+set_partitions(a);
+{{{1}, {2}, {3}, {4}}, {{1}, {2}, {3, 4}}, {{1}, {2, 3}, {4}}, {{1}, {2, 3, 4}}, {{1}, {2, 4}, {3}}, {{1, 2}, {3}, {4}},
+{{1, 2}, {3, 4}}, {{1, 2, 3}, {4}}, {{1, 2, 3, 4}}, {{1, 2, 4}, {3}}, {{1, 3}, {2}, {4}}, {{1, 3}, {2, 4}}, {{1, 3, 4}, {2}},
+{{1, 4}, {2}, {3}}, {{1, 4}, {2, 3}}}
+
+setdifference(a, b);
+{1, 3}
+
+emptyp(a);
+false
+
+elementp(2, a);
+true
+
+cardinality(a);
+4
+
+cartesian_product(a, b);
+{[1, 2], [1, 4], [1, 6], [1, 8], [2, 2], [2, 4], [2, 6], [2, 8], [3, 2], [3, 4], [3, 6], [3, 8], [4, 2], [4, 4], [4, 6], [4, 8]}
+
+subsetp(a, b);
+false
+
+symmdifference(a, b);
+{1, 3, 6, 8}
+
+partition_set(union(a, b), evenp);
+[{1, 3}, {2, 4, 6, 8}]
+
+c: setify(makelist(fib(n), n, 1, 20));
+{1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765}
+
+equiv_classes(c, lambda([m, n], mod(m - n, 3) = 0));
+{{1, 13, 34, 55, 610, 1597, 2584}, {2, 5, 8, 89, 233, 377, 4181}, {3, 21, 144, 987, 6765}}
+
+disjointp(a, b);
+false
+
+adjoin(7, a);
+{1, 2, 3, 4, 7}
+
+a;
+{1, 2, 3, 4}
+
+disjoin(1, a);
+{2, 3, 4}
+
+a;
+{1, 2, 3, 4}
+
+subset(c, primep);
+{2, 3, 5, 13, 89, 233, 1597}
+
+permutations(a);
+{[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2],
+ [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1],
+ [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1],
+ [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]}
+
+setequalp(a, b);
+false